# Classical Mechanics by Muhammad Usman Hamid

**Objectives of the course:**

To provide solid understanding of classical mechanics and enable the students to use this understanding while studying courses on quantum mechanics, statistical mechanics, electromagnetism, fluid dynamics, space-flight dynamics, astrodynamics and continuum mechanics.

We are really very thankful to Muhammad Usman Hamid for providing these notes and appreciates his effort to publish these notes on MathCity.org

Name | Classical Mechanics |
---|---|

Author | Muhammad Usman Hamid |

Pages | 309 pages |

Format | PDF (see Software section for PDF Reader) |

Size | 7.77 MB |

### Contents & Summary

- GENERAL INTRODUCTION AND NON INERTIAL REFERENCE SYSTEMS
- Introduction, basic definitions. Foucault“s Theorem, Newtonian Mechanics. Fundamental laws and principles of Mechanics.

- KINETICS
- Work, power, kinetic energy and energy principal, conservative force fields, conservation of energy theorem, impulse, torque. Conservation of linear and angular momentum. Atwood machine, Virial Theorem, Non-conservative forces. Motion of Particles under different phenomenon.

- KINEMATICS
- Basic definitions, Rectilinear motion of particles. Uniformly accelerated rectilinear motion. Curvilinear motion of particle, rectangular components of velocity and acceleration, tangential and normal components of velocity and acceleration, radial and transverse components of velocity and acceleration. Projectile motion with air resistance.

- RESISTED MOTION AND DAMPED FORCED OSCILLATOR
- Vertical motion with air resistance. Damped harmonic oscillator. Resonance frequency. Damped forced oscillations.

- CENTRAL FORCES AND PLANETARY MOTION
- Central force fields, equations of motion, potential energy, orbits. Kepler”s law of planetary motion. Apsides and apsidal angles for nearly circular orbits. Motion in an inverse square field. Escape velocity. Time varying mass system (Rockets)

- PLANER MOTION OF RIGID BODIES
- Introduction to rigid and elastic bodies, translations, rotations. Linear and angular velocity of a rigid body about a fixed axis, moments and products of inertia of various bodies including hoop or cylindrical shell, circular cylinder, spherical shell. Parallel and perpendicular axis theorem, Degrees of freedom, instantaneous axis and center of rotation, Motion of the center of mass, Euler“s theorem and Chasle”s theorem, Radius of gyration of various bodies

- MOTION OF RIGID BODIES IN THREE DIMENSIONS AND MOMEMNT OF INERTIA OF RIGID BODIES
- General motion of rigid bodies in space. Angular momentum and moment of inertia. Principal axes and principal moments of inertia. Determination of principal axes by diagonalizing the inertia matrix. Equimomental systems, Momental Ellipsoid.

- EULER EQUATIONS OF MOTION OF A RIGID BODY
- Accelerated coordinate systems and inertial forces, Rotating coordinate systems, Velocity and acceleration in moving system: Coriolis, Centripetal and transverse acceleration, Dynamics of a particle in a rotating coordinate system. Force free motion, Free rotation of a rigid body with an axis of symmetry, Rotating axes theorem. Euler“s dynamical equations. Free rotation of a rigid body with three different principal moments, torque free motion of a symmetrical top. The Eulerian angles, angular velocity and kinetic energy in terms of Euler angles, The Eulerian angles, Angular velocity and kinetic energy in terms of Euler angles, Space cone, Motion of a spinning top and gyroscopes- steady precession, Sleeping top